
----- Additional Notes about Toolkit for Interactive Mathematics ------

This file contains corrections and supplements to the Toolkit documentation
.
The name of this file is README.TXT; it is stored in the \TIM subdirectory.


RIGHT-CLICKING

Because the right mouse button is rarely used in Windows applications, but
is important in Toolkit, the following is restated here for emphasis:  when
you are instructed to 'right-click', click with the right mouse button
only, in the location described, which will be either the title bar of the
object or the object itself.


TWO BOOKS INCLUDED WITH TOOLKIT DOCUMENTATION

The larger loose-leaf document, the "Toolkit for Interactive Mathematics
Teacher Guide," is designed to give teachers and students a basic
introduction to Toolkit.  Its step-by-step tutorials in chapters 1 through
9 lead you through each of the components of the product.  The smaller
book, "Mathscript Reference", is more technical and is intended for those
wishing to gain a deeper understanding of the structure and philosophy of
MathKit, the underlying mathematics engine of Toolkit for Interactive
Mathematics.

MathKit is owned by University of North Carolina and licensed to
EduQuest for use in Toolkit for Interactive Mathematics.  Since
MathKit can potentially be included in other products, there are some
differences in vocabulary between the two publications.  For example, a
'TIMText' is an interactive mathematics exploration which you
can create with Toolkit for Interactive Mathematics.  The MathScript
Reference refers to the same interactive text by the more generic names,
'book' or 'MathKit book'.


ON-LINE HELP

There are two on-line help files included with this product:  TIM.HLP and
MATHKIT.HLP.  TIM.HLP contains the main on-line help which you will reach
when you click on Help, then Contents, from any Toolkit screen.  Items
which are associated with Toolkit for Interactive Mathematics only, such as
Algebra Tools and Data Tools, are included here.  The file MATHKIT.HLP
contains the on-line help called MathScript Reference, which you can reach
from several different menus, including the Help menu, and via a button
named MathScript in the main on-line help.

To get help on any of the MathScript commands and functions, select the
menu item named MathScript Reference, or click on the MathScript button in
the main on-line help.  For example, to learn more about the command named
Plot, reach the MathScript Reference via any the means mentioned in the
previous paragraph, then choose Search, then type the first letters of the
word (in this case Plot).

The menu selection called MathScript Reference brings up an on-line version
of the book with the same name which is part of the Toolkit documentation.


FUNCTIONS AND EXPRESSIONS

Functions and expressions are two of MathKit's mathematical objects.
Toolkit makes a distinction between functions and expressions, and
understanding this distinction is important for success with Toolkit.  A
MathScript command which expects a function as an argument should not be
given an expression, and vice versa.  For example, the command PLOT SQRT
graphs the function whose name is sqrt (square root).  On the other hand,
the command DIF SQRT(X),X displays the derivative of the expression sqrt(x)
with respect to x.  The command PLOT SQRT(X) (i.e., plot an expression) has
a different meaning (see 'plot expression' in Appendix B of the Teacher
Guide), and the command DIF SQRT,X will not be accepted.

You will become accustomed to this and other distinctions as you work
through the tutorials in the Teacher Guide, and additional discussion can
be found on pages 6-37,38 and in Appendix B of the Teacher Guide.


3-D GRAPH WINDOWS

3-D graph windows have changed slightly from the pictures shown in the
Teacher Guide, for example, on pages 8-27 and 10-8.  The difference is in
how you can change the viewing angle (latitude and longitude) of the 3-D
graph.

To change the view of a 3-D graph, click on the lower right corner of the
graph window and then (while still holding the mouse button) move the
cursor around the interior of the graph window.  You will see the viewing
angle change.  Release the mouse button to view the graph from the new
angle.


FACTORING

Only expressions in one variable can be factored, with the exception that
if the factoring only involves a common factor, there can be more than one
variable.  In order to factor polynomials correctly in Algebra Tools or
Data Tools, you must be in exact arithmetic mode with Expand Powers on (use
the Options Menu to set these.)  See also the following paragraphs.


COMMANDS WHICH REQUIRE EXACT ARITHMETIC

The two modes of arithmetic in Toolkit, decimal and exact, are described in
various places, including the MathScript Reference, the on-line help, and
Appendix D of the Teacher Guide.  The following commands should be used in
exact arithmetic mode:  FACTOR, DIF (or D), SIMPLIFY, EXPAND, SOLVE.

In Algebra Tools or Data Tools, switch to and from exact arithmetic from
the Options Menu.  Within a TIMText script, switch to exact arithmetic with
the command READLONG, and switch back with READFLOAT.


COMMANDS WHICH REQUIRE DECIMAL ARITHMETIC

Three customized commands which relate to fitting a straight line to data
must be used in decimal arithmetic mode.  The commands are LEASTSQUARE,
RESIDUAL, and SHOWRESID in the file named DATA.  These commands are
designed for use within TIMTexts or Data Tools, where the default mode is
decimal arithmetic.  To use them within Algebra Tools, switch to Exact
Arithmetic in the Options menu.  Customized commands are discussed further
in the next paragraphs, and in Chapter 7 of the User Guide.


INPUT CHECKING

The inputs to MathScript commands and functions are checked to ensure that
they are the right form.  For example, an unrecognized color name for
PENCOLOR or a negative input to the logarithm function will be rejected.
However, the same is not necessarily true for customized commands which you
build yourself from the MathScript vocabulary.  You should not expect the
same protection from bad inputs when you use the customized commands or
functions which are included with this product, or those which you create.

However, it is possible to build input-checking into your definition of a
customized command.  To see an example of this, study how it was
accomplished in the program which defines the function named PERMUTE in the
MET file.  Chapter 7 of the Teacher Guide shows how to use, view, change,
create, and save customized commands.


SETTING THE REFINEMENT FOR PLOTTING AND EQUATION SOLVING

The word 'refinement' is used in Toolkit as a measure of how many
calculations are done when a graph or an equation is plotted, or when the
roots of an equation are estimated.  When you increase the refinement, the
resulting answer or graph will be more accurate, but at the price of
increased computation time.

For plotting in two dimensions, a satisfactory refinement for plotting
equations will probably be between 20 and 100, and for plotting functions,
from 50 to 250.  For plotting in three dimensions, a satisfactory
refinement would be between 10 and 40.

For solving equations, Toolkit uses an enhanced bisection method, and
refinement normally need not be over 50 to get 7 place accuracy, and it
usually can be much less.

On some computers, extremely high values of refinement (over 400) when
plotting or solving equations can cause a system failure which will require
you to restart the computer.


GRAPHING FUNCTIONS WITH HIGH-EXPONENT DENOMINATORS

The upper limits will differ on different computers, but the general idea
is that functions like 1/xªn will not graph for n larger than 7.  Use
negative exponents in the definition of the function to avoid this
limitation.


RESERVED WORDS

Refer to the list on page 62 of the MathScript Reference book.  Using these
words as the name of a mathematical object (function, expression, etc.) can
have unexpected consequences.


THE SELF DOCUMENTING FEATURE OF MATHSCRIPT

On page 94 of MathScript Reference you will see that the simple command
GRAPH SIN will plot the sine curve in the active graph window, using
default values of pen color and pen width.  However, it is also possible to
specify these values within the command itself, for example:
DRAW THE GRAPH OF SIN USING COLOR RED WIDTH 3 REFINEMENT 80 IN "MYGRAPH"

Optional words like 'draw', 'the', and 'of' make this example read more
clearly.  The precise definition of what words are required and optional is
included in the first part of the description of the graph command on that
page.  The key to the symbols used in the syntax description is in section
5.8.1 on page 28.


INPUTS TO FLOATING POINT FUNCTIONS

Toolkit's mathematics functions (cos, sqrt, exp, etc.) are floating point
functions which accept inputs with up to seven significant figures.  If the
input exceeds this precision, accuracy is lost.  For example, the function
floor produces the greatest integer less than the input.  Floor(6.999999)
correctly  produces 6, but floor(6.9999999) produces 7 because the input is
rounded to seven significant figures before the function is called.


ERROR MESSAGE TOO LARGE - SYSTEM SEEMS TO FREEZE

In rare circumstances, the OK button of an error message display is off the
screen, so that it seems that you have lost the ability to do use the
keyboard or the mouse.  If this happens, press <Esc> (Escape).  The Escape
key will also stop a computation if desired.


THE EXPERT SYSTEM AND RULE SETS

Factoring, simplification, and equation solving are handled in Toolkit
through MathKit expert systems.  While it is possible to view and even
change the rule sets which the expert systems use, this is not documented
or supported by EduQuest.  People wishing to explore this aspect further
should contact Dr. James E. White at either of the addresses indicated
under "Feedback and Discussion" below.


'UNDEFINING' A VARIABLE

If a variable (for example, with name 'height') has been assigned a value
(as a function, expression, vector, etc.) and you wish to remove this
assignment and return it to its original state, issue this command at the
command line or in a script:  MAKE VARIABLE HEIGHT


CORRECTIONS TO THE TEACHER GUIDE

Teacher Guide, page 5-3 and 10-7:  In these and other locations in the
Teacher Guide, the menu for the 2D graph window is different from what you
will see on the screen.  The menu now contains these new items: 'Wallpaper'
and 'Sprite".  The contents of 'Wallpaper' were formerly found under
the 'File' menu item, which is now gone.  The contents of 'Sprite' were
formerly found under the 'Utilities' menu.  The contents and function of
these menu items have not changed.

Teacher Guide, page 6-25:  The new version of the Substitute dialog box
does not match the picture.  It is now possible to substitute within
vectors (for example to change a parametrically defined function), and this
option is now included in the dialog box.

Teacher Guide, page B-15 (Appendix B):  The example for the command
surfrefinement should read as follows: surfrefinement 20.

Teacher Guide, page H-5 (Appendix H):  The list of files included with
Toolkit needs one correction:  The file named MKMEM.DLL is now named
MWMEM.DLL.


FEEDBACK AND DISCUSSION

Your questions and comments are invited.  To discuss the MathScript
Reference and MathScript itself, contact the author, Dr. James E. White, at
the address given on page ii of the book entitled "MathScript Reference."

To discuss the possibility of sharing teaching ideas and TIMTexts created
by other teachers and students, and to find out how to contribute your own,
use the Internet address listed on page A-1 (Appendix A) of the Teacher
Guide.


